Who's fantasising now? Not, for some little time at least, the man who said he could step out of a crazy spiral of Premier League spending and announce himself a sure-fire contender one of these years.

Not Arsène Wenger, not the man who yesterday woke up from almost everyone else's nightmare view of the future of Arsenal with a performance that in the end was beautifully balanced between defensive security and a cutting edge that so many feared had left town with Robin van Persie.

For Wenger it was the other side of the trauma that afflicted his beaten rival, Brendan Rodgers of Liverpool. The new man at Anfield, like his conqueror yesterday, has a single vision of how you play football, and how you can turn it into a winning formula, and if he wasn't sure about the level of nerve that will be required in the next few weeks and months, this was not only a defeat of the most wounding kind it was – judging by his expression on the touchline – also a somewhat shocking revelation.

With one point from three matches, with the club rooted in the bottom three, alongside QPR, after Liverpool's worst start in 50 years, and alarming signs of metal fatigue in such former titans as Pepe Reina and Steven Gerrard, last season's hero at Swansea could do no better than reassert his belief in certain football values.

The man who was bold enough to declare that Andy Carroll had no place in his pattern for the future, and then found himself critically short of cover at the front, had no option but to declare that this was not an occasion to pass judgement on anything other than a collective failure to produce an adequate performance. Such a statement duly came from a man who could scarcely have stripped himself more comprehensively of anything resembling a comfort zone.

If he needed any more ballast on a day when only his faith in the precocious Raheem Sterling and his Swansea protégé Joe Allen had offered anything much like a hint of redemption, it was that for some years now Wenger has been occupying the same dangerous country, out on his own and, according to so much received wisdom, a prisoner of his own principles. If this was ever true, yesterday was when, with the help of his new signings Santi Cazorla and Lukas Podolski, he broke out of jail.

Already Cazorla had announced himself an investment of potentially transforming brilliance, a man who might be heading toward the wrong side of his twenties but whose pedigree in the margins of the great era of Spanish football suggested extreme value at a mere £15m.

Podolski also has formidable form down the years, of course, but for Wenger the aching speculation came with the question of whether he and Cazorla could reanimate themselves in the new theatre of the Premier League. Against Liverpool this particular doubt perished in a move of quite superb cohesion.

When Gerrard fired a wayward pass, Podolski and Cazorla not only punished cruelly the England captain but also laid waste an entire team. Rodgers had every reason to stare at his immaculate polished shoes. His hopes for some kind of statement in an early, perhaps pivotal, challenge were not so much threatened as engulfed.

The Liverpool manager could, if he cared to, write off Arsenal's second strike, this one from Cazorla after his superb contribution to Podolski's opener, as a fresh example of Reina's current agony of failing confidence but it wasn't much of a hiding place.

Arsenal were the better team by a huge distance and if Olivier Giroud had not marred some otherwise impressive work with another of those misses which linger in the mind, the fact would have been still more brutally underlined. As it was, Arsenal looked like a team nicely ripening into something resembling their old rosy glow.

Before the game Wenger had made one of those statements of his which tend to provoke nothing quite so much as mirth when the agent community give us their version of long-term realities. "We [Arsenal] are run in a very responsible way," he declared. "We make a profit every year. In a Europe where nearly everybody is struggling we find ourselves a little bit in the situation of Germany in the European economy."

Around lunchtime yesterday it seemed like an announcement guaranteed to provoke a fusillade of returned season tickets. But that was before Cazorla and Podolski took Arsenal back to at least a little bit of the best of themselves – and Abou Diaby confirmed Wenger's assessment that, if he is fragile, he is also a player capable of immense impact.

It will take rather more, of course, to suggest a full-blown renaissance but here were flashes of something which it had not been unreasonable to fear might just have been permanently mislaid. Certainly, we could only speculate on quite how much Brendan Rodgers would have given for such a glimpse into the future.